Re: R structure in bivariate analysis

Dear Peter,

In the typical situation, ASReml expects will will have to invert the
variance structures and it cannot invert
a variance of ZERO. Therefore if you supply an iniutal value of ZERO for
a variance, ASReml will
plug in some other value. However, a covariance of ZERO is allowed
because that does not make the matrix uninvertable.
(If it is too BIG, it will make it negative definite, and for some
particular values make the matrix singular but these
are not immediately obvious and are trapped elsewhere.

In your situation, since there is no information in the data on these two
particular variances,
it does not matter what value is supplied. However, you need to FIX it
(!GFFP) or you will get a singularity
in the AI matrix. ASReml recognises that the value is not needed and does
not use it.

However, it doesn't realize it doesn't need it at the beginning and so
enforces that it not be ZERO.

Changing
1221 0 IDEN
Trait 0 US 0.8250 0.0 0.1E-7 !GUFF

to
1221 0 IDEN
Trait 0 US 0.8250 0.0 0. !GUFF

failed because ASReml ignores (doesn't see; I won't try and explain WHY)
the zero values and so goes looking
for two more parameters on the next line (but that says
3519 0 IDEN

so the initial values are 0.825 3519 0
and it will fall over reading the next line, being now out of step.

If you used the form
1221 0 IDEN
Trait 0 US !GUFF
0.8250 0.0 0.

I expect it would work (and replace the variance of 0. with some positive
number).

I trust this helps.

May Jesus Christ be gracious to you in 2008,

Arthur Gilmour, His servant .
 
Mixed model regression mapping for QTL detection in experimental crosses.
Computational Statistics and Data Analysis 51:3749-3764 at
http://dx.doi.org/10.1016/j.csda.2006.12.031

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Peter Adam <peter.j.adam_at_GMAIL.COM>
Sent by: ASReml users discussion group <ASREML-L_at_AGRIC.NSW.GOV.AU>
18/06/2008 07:39 PM
Please respond to
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Subject
R structure in bivariate analysis

Dear Auther and others:
 
I am working on bivariate analysis using tree (or animal) model
and in a puzzle about the R structure. In my data, trait A was
measured at sites 2-3-4, and trait B was measured at sites 1-3-4.
I would like to fit heterogeneous residual variances for different
sites. I therefore set the covariances to 0 for sites 1 and 2,
and also fix the variances to 0 for the combinations of site and
trait without data.
 
I first tried the following code:
 
!PART 1
trait_a trait_b ~ Trait Tr.site !r Tr.site.rep Tr.tree Tr.site.fam
4 2 3
1200 0 IDEN
Trait 0 US 0.1E-7 0.0 0.6748 !GFFU
1221 0 IDEN
Trait 0 US 0.8250 0.0 0.1E-7 !GUFF
3519 0 IDEN
Trait 0 US 0.8242 0.2106 0.5981
3507 0 IDEN
Trait 0 US 0.8286 0.2127 0.6065
......
 
and it worked as I expected:
 
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.1000E-07 0.000
  0.000 0.6741
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.8353 0.000
  0.000 0.1000E-07
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.8245 -0.1306
-0.9180E-01 0.5996
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.8289 -0.7723E-01
-0.5487E-01 0.6090
 
Then I changed the residual variance for trait A at site 1 from
0.1E-7 to 0.0.
 
!PART 2
trait_a trait_b ~ Trait Tr.site !r Tr.site.rep Tr.tree Tr.site.fam
4 2 3
1200 0 IDEN
Trait 0 US 0.0 0.0 0.6748 !GFFU
1221 0 IDEN
Trait 0 US 0.8250 0.0 0.1E-7 !GUFF
3519 0 IDEN
Trait 0 US 0.8242 0.2106 0.5981
3507 0 IDEN
Trait 0 US 0.8286 0.2127 0.6065
......
 
I noticed that instead of fixing it to 0, ASReml filled the first
variance with a non-zero value (0.3885):
 
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.3885 0.000
  0.000 0.6741
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.8353 0.000
  0.000 0.1000E-07
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.8245 -0.1306
-0.9180E-01 0.5996
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.8289 -0.7723E-01
-0.5487E-01 0.6090
 
I further changed the another 0.1E-7 to 0 as well, and ASReml failed
with the message: "REQUIRE !ASUV qualifier for this R structure". The
error message changed to "Error structures are wrong size" once I used
!ASUV qualifier (and added !f mv in the model as well).
 
So, how does ASReml treat 0s in R structure? What is the real
difference between 0 and a very small number like 0.1E-7? Why 0s are
ok for covariances but not for variances?
 
Thanks!
Peter Adam
Received on Sat Jun 19 2008 - 12:43:21 EST